Question: Simplify the following expression: $ z = \dfrac{-6n + 2}{-5n} + \dfrac{3}{8} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{8}{8}$ $ \dfrac{-6n + 2}{-5n} \times \dfrac{8}{8} = \dfrac{-48n + 16}{-40n} $ Multiply the second expression by $\dfrac{-5n}{-5n}$ $ \dfrac{3}{8} \times \dfrac{-5n}{-5n} = \dfrac{-15n}{-40n} $ Therefore $ z = \dfrac{-48n + 16}{-40n} + \dfrac{-15n}{-40n} $ Now the expressions have the same denominator we can simply add the numerators: $z = \dfrac{-48n + 16 - 15n}{-40n} $ $z = \dfrac{-63n + 16}{-40n}$ Simplify the expression by dividing the numerator and denominator by -1: $z = \dfrac{63n - 16}{40n}$